Strain relaxation in ${\text{Fe}}_3{\text{O}}_4/{\text{MgAl}}_2{\text{O}}_4$ heterostructures: Mechanism for formation of antiphase boundaries in an epitaxial system with identical symmetries of film and substrate

Strain relaxation studies in epitaxial magnetite, ${\text{Fe}}_3{\text{O}}_4$, thin films grown on ${\text{MgAl}}_2{\text{O}}_4$(100) substrates are reported. The study shows that the films were relaxed in line with the theoretical model prediction with a critical thickness, $t_{\text{c}}=5\text{nm}$. Antiphase boundaries (APBs) are not expected to form in ${\text{Fe}}_3{\text{O}}_4$ films grown on ${\text{MgAl}}_2{\text{O}}_4$ substrates because both film and substrate have the same crystal symmetry. In contrast, our study reveals the formation of APBs within the ${\text{Fe}}_3{\text{O}}_4$ films. Our analysis shows that the APBs in a ${\text{Fe}}_3{\text{O}}_4/{\text{MgAl}}_2{\text{O}}_4$ heteroepitaxial system are formed by partial dislocations, which accommodate the misfit. This formation mechanism of APBs is fundamentally different from the one found in the ${\text{Fe}}_3{\text{O}}_4/\text{MgO}$ system, where APBs are formed as a consequence of equivalent nucleation sites on the MgO substrate separated by nontranslational vectors of the ${\text{Fe}}_3{\text{O}}_4$ lattice. The mechanism for the formation of antiphase boundaries through partial dislocations should be applicable to a wide range of epitaxial systems having identical symmetries of the film and the substrate and significant lattice mismatch.

Figure 1

(a) The $\omega \text{−}2\theta$ scans performed on 15, 60, and 120 nm ${\text{Fe}}_3{\text{O}}_4$ films grown on (100) ${\text{MgAl}}_2{\text{O}}_4$ substrate measured for symmetric (400) Bragg reflection. Curves are shifted on the vertical axis for clarity. (b) The $\omega \text{−}n\theta$ scans performed on 60 and 120 nm ${\text{Fe}}_3{\text{O}}_4$ films grown on (100) ${\text{MgAl}}_2{\text{O}}_4$ substrate measured for asymmetric (622) Bragg reflection (measured in the grazing exit geometry).

Figure 2

TEM dark field images in plan view of (a) 70 and (b) 200 nm ${\text{Fe}}_3{\text{O}}_4$ films on ${\text{MgAl}}_2{\text{O}}_4$ substrate. According to the (220) imaging conditions chosen, APBs with shift vector $\frac{1}{4}\left[110\right]$ appear bright.

Figure 3

Cross-sectional TEM bright field images of 70-nm-thick ${\text{Fe}}_3{\text{O}}_4$ film on ${\text{MgAl}}_2{\text{O}}_4$ substrate. Misfit dislocations are seen at the interface, when a two-beam imaging conditions with a (040) imaging vector is established (a). Under (004) imaging conditions (b) the dislocation contrast vanishes. Contrast fluctuations within the ${\text{Fe}}_3{\text{O}}_4$ layer are caused by strain and/or APBs.

Figure 4

(Color online) High-resolution TEM image of the interfacial region between ${\text{Fe}}_3{\text{O}}_4$ and ${\text{MgAl}}_2{\text{O}}_4$. The Burgers circuit indicates a closing vector of $\frac{1}{4}\left[010\right]$. This Burgers vector component seen in the (100) projection does not comply with a translation vector of the lattice, i.e., a partial dislocation is formed. Accordingly, an antiphase boundary is formed between the left and right parts of the figure. Due to local strain fields neither the atomic structure of the dislocation core nor that of the APB are resolved. Unit cells of ${\text{Fe}}_3{\text{O}}_4$ and ${\text{MgAl}}_2{\text{O}}_4$ are schematically displayed as insets (Fe: red, O: yellow, Mg: green, Al: blue).

Figure 5

Comparison of experimentally observed values of the in-plane strain, ${\epsilon }_{\parallel }$, with the FKR model predictions for the ${\text{Fe}}_3{\text{O}}_4$ films grown on ${\text{MgAl}}_2{\text{O}}_4$ (100) substrates as a function of thickness. The solid line is the theoretical prediction and scattered points are experimentally observed values.

Figure 6

(Color online) Schematic of the APB observed by high-resolution TEM (Fig. 4). The formation of the misfit dislocation with a Burgers vector component of $\frac{1}{4}\left[010\right]$ in the (100) plane, results in an APB within the ${\text{Fe}}_3{\text{O}}_4$ film, which is indicated by the arrow. (Fe: red, O: yellow, Mg: green, Al: blue).